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In HILO microscopy, a highly inclined and laminated light sheet is used to illuminate the sample, thus drastically reducing background fluorescence in wide-field microscopy, but maintaining the simplicity of the use of a single objective for both illumination and detection. Although the technique has become widely popular, particularly in single-molecule and super-resolution microscopy, a limited understanding of how to finely shape the illumination beam and how this impact on the image quality complicates setting HILO to fit the experimental needs. In this work, we build up a simple and comprehensive guide to optimize the beam shape and alignment in HILO and to predict its performance in conventional fluorescence and super-resolution microscopy. We model the beam propagation through Gaussian optics and validate the model through far- and near-field experiments, thus characterizing the main geometrical features of the beam. Further, we fully quantify the impact of a progressive reduction of the inclined beam thickness on the image quality of both diffraction-limited and super-resolution images and we show that the most relevant impact is obtained by reducing the beam thickness to sub-cellular dimensions (< 3 μm). Based on this, we present a simple optical solution to reduce the inclined beam thickness down to 2.6 μm while keeping a field-of-view dimension suited for cell imaging and allowing an increase in the number of localizations in super-resolution imaging of up to 2.6 folds.

This paper contributes to studying the bifurcations of closed invariant curves in piecewise-smooth maps. Specifically, we discuss a border collision bifurcation of a repelling resonant closed invariant curve (a repelling saddle-node connection) colliding with the border by a point of the repelling cycle. As a result, this cycle becomes attracting and the curve is destroyed, while a new repelling closed invariant curve appears (not in a neighborhood of the previously existing invariant curve), being associated with quasiperiodic dynamics. This leads to a global restructuring of the phase portrait since both curves mentioned above belong to basin boundaries of coexisting attractors.

Mechanical transitions in molecular motors often occur on a submillisecond time scale and rapidly follow binding of the motor with its cytoskeletal filament. Interactions of nonprocessive molecular motors with their filament can be brief and last for few milliseconds or fraction of milliseconds. The investigation of such rapid events and their load dependence requires specialized single-molecule tools. Ultrafast force-clamp spectroscopy is a constant-force optical tweezers technique that allows probing such rapid mechanical transitions and submillisecond kinetics of biomolecular interactions, which can be particularly valuable for the study of nonprocessive motors, single heads of processive motors, or stepping dynamics of processive motors. Here we describe a step-by-step protocol for the application of ultrafast force-clamp spectroscopy to myosin motors. We give indications on optimizing the optical tweezers setup, biological constructs, and data analysis to reach a temporal resolution of few tens of microseconds combined with subnanometer spatial resolution. The protocol can be easily generalized to other families of motor proteins.

Here we propose a method for studying the distribution of genetic material inside a prokaryotic cell by implementing Fluorescence In Situ Hybridization (FISH) with single molecule sensitivity and 3D nanometric localization to map the position of ribosomes and selected gene loci.

We show a new technique that we developed for 3D tracking of single fluorescent molecules inside living cells with nanometer accuracy. To account for the optical sectioning of thick samples we built up a HILO (Highly-Inclined-and-Laminated-Optical-sheet) microscopy system [1], through which we can excite the sample in a widefield configuration by a thin sheet of light, spanning the entire thickness of the cell with a SNR much higher than traditional WF microscopy. Under these illumination conditions, we apply a method capable of reaching nanometer x, y, z localization by exploiting the properties of the point-spread-function of out-of-focus fluorescent probes.

Forewords The European Conference on Iteration Theory, ECIT 2010, has been held on September 2010, 12-17, in Midi-Pyrenees, France. It was organized at “Le Roc nantais”, in Nant, Aveyron, by the “Institut National des Sciences Appliquees de Toulouse” (INSA) with the help of the Conseil Regional of Midi-Pyrenees and the Laboratory for Analysis and Architecture of Systems (LAAS). ECIT 2010 followed the sequence of meetings started in Toulouse 1973 and continued in Graz, Austria, 1977, Marburg, Germany, 1980, Toulouse, France, 1982, Lochau, Austria, 1984, Caldes de Malavella, Spain, 1987, Batschuns, Austria, 1989, Lisboa, Portugal, 1991, Batschuns, Austria, 1992, Opava, Czech Republic, 1994, Urbino, Italy, 1996, Muszyna, Poland, 1998, La Manga del Mar Menor, Spain, 2000, Evora, Portugal, 2002, Batschuns, Austria, 2004, Gargnano, Italy, 2006 and Yalta, Ukraine, 2008. The main topic of ECIT is iteration theory. This theory is a branch of mathematics and includes topics related to discrete dynamical systems and functional equations. The aim of these theoretical studies is to model, analyze and understand iterative process, for example, systems with discrete time. Such systems can be obtained from many different fields of application: engineering (control theory, electronics,...), physics, mechanics, economics, biology, ecology, ... All these questions have given rise to the introduction and the development of several branches of mathematics, related with the iteration theory, as, for instance:  Theory of singularities  Bifurcation theory  Dynamical systems with small perturbations  Topological dynamics  Ergodic theory  Symbolic dynamics  Embedding problems  Iteration theory, in particular also iteration groups and semi-groups  Iterative and linear functional equations In this ECIT 2010 conference, there were 73 participants, issued from many different countries including Algeria, Austria, China, Czech Republic, Germany, India, Israel, Italy, Poland, Portugal, Russia, Spain, Tunisia and Ukraine. 57 talks have been given and there were many very fruitful exchanges and discussions during the special sessions “Problems and remarks” and during the whole conference. The present issue of ESAIM Proceedings gathers 18 contributions by participants to the ECIT 2010 conference. These papers are related to the different thematics, which have been proposed during the conference, among them, symbolic dynamics, dynamical systems, functional equations, bifurcation theory,... We thank all authors for their contribution to this issue of ESAIM Proceedings.

In this paper we analyze the working of a capitalist system with sophisticated financial institutions, where the Modigliani-Miller theorem does not apply, so that the financial part of the economy affects the working of the real side. This model, in which the real and the financial sectors are connected throught a simple portfolio approach, and where the ratio between cash flow and debt commitment affects the pace of investment, explains the emergence of instability and, more generally, the cyclical behavior of the economy as an internally generated phenomenon of a capitalist system. As far as the dynamic behavior of the model is concerned, we can envisage the following process: when investment activity is low, the system evolves toward a stationary state; as soon as the accumulation rate starts growing, the model shows the existence of limited cycles and, when the elasticity of investment to internal finance increases further, a chaotic dynamic appears. Finally, we expect a situation of financial crisis to emerge when the elasticity of investment to internal financing constraint goes beyond a certain level, i.e. when the realized flow of profits is not sufficiently high to validate the debt commitments. The working of the model is referred to an economics with no technical change, while its dynamic properties will be investigated by the use of numerical simulation.

A general investigation of the heart pulse propagation in blood vessel has been done and this research has been conducted for the blood flow in physiological conditions; then also the problems connected to new surgical techniques and also necessary in the organs transplantations. In particular in presence of insertion at some distance from the input is investigated and also the effects of the connection of vascular segments with different mechanical properties increases the risk of generation of blood turbolence fluxes and involves, in the arterial vessels. Mechanical models of cardiovascular system have been studied and the effects considered in clinical applications.

For a truncated triadic model of the barotropic vorticity equation of two-dimensional rotating fluid the mechanism of successive bifurcations to chaotic attractors is evidentiated. It is suggested that the transition to chaos takes place through a Feigenbaum sequence.

It is shown that in a suitable class of Lotka-Volterra systems it is possible to characterize the centre-critical case of the Hopf bifurcation of the multipopulation equilibrium. Moreover, for three populations, it is shown that, in the non-critical case, Hopf bifurcation is supercritical. Numerical evidence of transition to chaotic dynamics, via period-doubling cascades, from the limit cycle is reported.

In a low-order model of barotropic, quasi-geostrophic flow on a rotating atmosphere, representing an arbitrary forced zonal flow interacting with two waves, hysteretic cycles are shown and steady and periodic regimes coexisting with chaotic regimes, along suitable paths in the space of the control parameters, forcing intensity and absolute rotation.

The three-dimensional cyclically invariant Lotka–Volterra map is studied, pointing out, by analytic and numeric techniques, the bifurcations of fixed points that have no counterpart in the corresponding system of ordinary differential equations. In particular, the Hopf-bifurcation of the three-population equilibrium point, and the related dynamics in a bounded invariant domain, are analysed. The analytic description of stable periodic orbits in a weak-resonant case is given, and the transitions to chaotic attractors via sequences of Hopf-bifurcations and period-doublings are discussed.

We analyse the bifurcations occurring in the attracting set of a system of three ordinary differential equations representing a minimal model for forced, dissipative, two-dimensional flows in a rotating fluid, as the rotation parameter is varied. In particular, we point out the transitions from steady states to chaotic attractors via sequences of period-doubling bifurcations, similar to those found in unimodal, unidimensional maps, as revealed by the study of the return map on a global surface of section for the flow.

The Rossler system of equations is studied by both analytic and numerical techniques. The appearance of limit cycles in one-parameter families, not related to a Hopf bifurcation, is explained by the analysis of the model in the full parameter space. Domains in the parameter space leading to sequences of period-doubling and transition to chaotic attractors are identified. The analysis of the return map associated with bifurcating limit cycles gives evidence that such transitions exhibit typical features of period-doubling cascades in unimodal maps of the interval.

An algorithm which gives very good first trial values for the computation of chemical equilibrium composition is proposed. It is based on writing the chemical reactions in “canonical form” and changing the independent component set until it is formed by the species present in greatest quantity at equilibrium. The advancement degrees ξr of the reactions are calculated considering the reactions to occur independently of any other. By applying a similar procedure to the series reactor method, a new powerful solution algorithm of the Rosenbrook's type is obtained. In the first method we linearize the equilibrium equations written making null the gradient of the free energy of the system with respect to the corresponding ξr whilst in the second one we make successive unidimensional searches solving the equations for ξr

In systems of ordinary differential equations representing the truncation to any order of the spectral, barotropic vorticity equation for two‐dimensional flows in rotating fluids, subject to constant forcing and dissipation, large values of absolute rotation inhibit the occurrence of equilibrium states other than the basic, forced regime, and promote transitions to periodic oscillations, via Hopf bifurcation.

In a previous paper Tramontana et al. (2009), we developed a three-dimensional discrete-time dynamic model in which two stock markets of two countries, say H(ome) and A(broad), are linked via and with the foreign exchange market. The latter is modelled in the sense of Day and Huang (1990), i.e. it is characterized by a nonlinear interplay between technical traders (or chartists) and fundamental traders (or fundamentalists). In the absence of connections, the foreign exchange market is driven by the iteration of a one-dimensional cubic map, which has the potential to produce a regime of alternating and unpredictable bubbles and crashes for sufficiently large values of a key parameter, which captures the speculative behavior of chartists. Such a dynamic feature, first observed and explained by Day and Huang (1990) in their stylized model of financial market dynamics, can be understood with the help of bifurcation analysis: an initial situation of bi-stability (two coexisting, attracting non-fundamental steady states around an unstable fundamental equilibrium) evolves into coexistence of cycles or chaotic intervals within two disjoint bull and bear regions, which eventually merge via a homoclinic bifurcation. By introducing connections between markets (i.e. by allowing stock market traders to be active abroad), the endogenous fluctuations originating in one of the markets spread throughout the whole three-dimensional system. It therefore becomes interesting to investigate how the coupling of the markets affects the bull and bear dynamics of the model. With regard to this, in Tramontana et al. (2009) we already performed a thorough analytical and numerical study of two simplified lower-dimensional cases, where connections are either totally absent (each market evolves according to an independent one-dimensional map) or occur in one direction (a two-dimensional system evolves independently of the third dynamic equation). Also a short analysis of the stability of the equilibria of the three-dimensional model was there started, arguing that the global (homoclinic) bifurcations may still be a characteristic of the dynamics. This investigation is precisely the object of the present paper. We shall analyze the dynamic behavior of the complete three-dimensional model, following the approach adopted in Tramontana et al. (2009), based mainly on the numerical and graphical detection of the relevant global bifurcations. Although analytical conditions for such global bifurcation, mainly homoclinic bifurcations, are difficult to be formalized, their existence and occurrence can be numerically detected. As it is standard in the qualitative study of dynamic behaviors, the transverse crossing between stable and unstable sets of unstable cycles, leading to homoclinic trajectories, give numerical tools which may be considered as proofs in a given numerical example.

We develop a three-dimensional nonlinear dynamic model in which the stock markets of two countries are linked through the foreign exchange market. Connections are due to the trading activity of heterogeneous speculators. Using analytical and numerical tools, we seek to explore how the coupling of the markets may affect the emergence ofbull and bearmarket dynamics. The dimension of the model can be reduced by restricting investors' trading activity, which enables the dynamic analysis to be performed stepwise, from low-dimensional cases up to the full three-dimensional model. In our paper we focus mainly on the dynamics of the one- and two- dimensional cases, with numerical experiments and some analytical results, and also show that the main features persist in the three-dimensional model.

In this paper a nonlinear discrete-time business cycle model of Kaldor-type is considered, to illustrate particular global bifurcations which determine the appearance or disappearance of attracting and repelling closed invariant curves. Such bifurcations sequences, which involve homoclinic tangencies and transversal intersection of the stable and unstable manifolds of saddle cycles, may increase the complexity of the basins of attraction of multiple, coexisting attractors. Particularly, for the business cycle model examined here, such dynamic phenomena explain the co-existence of two stable steady states and an attracting closed curve, with an intricate basin structure, for wide ranges of the parameters.

Empirical evidence has suggested that, facing different trading strategies and complicated decision, the proportions of agents relying on particular strategies may stay at constant level or vary over time. This paper presents a simple "dynamic market fraction" model of two groups of traders, fundamentalists and trend followers, under a market maker scenario. Market mood and evolutionary adaption are characterized by fixed and adaptive switching fraction among two groups, respectively. Using local stability and bifurcation analysis, as well as numerical simulation, the role played by the key parameters in the market behaviour is examined. Particular attention is paid to the impact of the market fraction, determined by the fixed proportions of confident fundamentalists and trend followers, and by the proportion of adaptively rational agents, who adopt different strategies over time depending on realized profits. © 2005 Elsevier Ltd. All rights reserved.

Il dibattito e gli studi sul Land Grab hanno permesso di dare visibilità ad una dinamica politica preoccupante seppur antica, che ha assunto nuove forme, tecniche e intensità nel contesto contemporaneo; ma l’attenzione isolata alla terra porta con sé però anche il rischio di rendere “invisibili” le forme complesse e diversificate di accaparramento e dispossessione, che sono interdipendenti e relazionate alla terra. Vorrei qui problematizzare la nozione di Land Grab proprio per rendere esplicite le molteplici catene di dipendenze che l’acquisto o il controllo della terra, in modo delocalizzato da parte di stati nazionali ed imprese multinazionali, causano e rimangono nascoste spesso nei dibattiti attuali: l’appropriazione della terra è spesso un furto d’acqua, è leva per il controllo di manodopera a basso costo, è una nuova ed esogena disciplina delle risorse simboliche e materiali nelle produzione agricola.

The Sharpe-Lintner-Mossin (Sharpe 1964; Lintner 1965; Mossin 1966) Capital Asset Pricing Model (CAPM) plays a central role in modern finance theory. It is founded on the paradigm of homogeneous beliefs and a rational representative agent. However, froma theoretical perspective this paradigmhas been criticized on a number of grounds, in particular concerning its extreme assumptions about homogeneous beliefs, information about the economic environment, and the computational ability on the part of the rational representative economic agent. The impact of heterogeneous beliefs among investors on the market equilibrium price has been an important focus in the CAPM literature. A number of models with investorswho have heterogeneous beliefs have been previously studied. 1 A common finding in this strand of research is that heterogeneous beliefs can affect aggregate market returns. However, the question remains as to how exactly does heterogeneity affect themarket risk of risky assets? In much of this earlier work, the heterogeneous beliefs reflect either differences of opinion among the investors2 or differences in information upon which investors are trying to learn by using some Bayesian updating rule.3 Heterogeneity has been investigated in the context of either CAPM-like mean-variancemodels (for instance, Lintner 1969; Miller 1977;Williams 1977; and Mayshar 1982) or Arrow-Debreu contingent claims models (as in Varian 1985;Abel 1989; 2002; and Calvet et al. 2004). © 2010 Springer-Verlag Berlin Heidelberg.

A discrete-time dynamic model of a financial market is developed, where two types of agents, fundamentalists and chartists, allocate their wealth between two risky assets and a safe asset, according to one-period mean-variance maximization. The two groups of agents form different expectations about asset returns and their variance/covariance structure, and this results in different demand functions. At the end of each trading period, agents' demands are aggregated by a market maker, who sets the next period prices as functions of the excess demand. The model results in a high-dimensional nonlinear discrete-time dynamical system, which describes the time evolution of prices and agents' beliefs about expected returns, variances and correlation. It is shown that the unique steady state may become unstable through a Hopf-bifurcation and that an attracting limit cycle, or more complex attractors, exist for particular ranges of the key parameters. In particular, the two risky assets may exhibit "coupled" long-run price fluctuations and time-varying correlation of returns. © 2005 Springer-Verlag Berlin Heidelberg.

This paper considers a discrete-time model of a financial market with one risky asset and one risk-free asset, where the asset price and wealth dynamics are determined by the interaction of two groups of agents, fundamentalits and chartists. In each period each group allocates its wealth between the risky asset and the safe asset according to myopic expected utility maximization, but the two groups have heterogeneous beliefs about the price change over the next period: the chartists are trend extrapolators, while the fundamentalists expect that the price will return to the fundamental. We assume that investors have CRRA utility, so that their optimal demand for the risky asset depends on wealth. A market maker is assumed to adjust the price at the end of each trading period, on the basis of the excess demand and according to particular stabilization policies. The model results in a three-dimensional nonlinear discrete-time dynamical system, with growing price and wealth processes, but it is reduced to a stationary system in terms of asset returns and wealth shares of the two groups. It is shown that the long-run market dynamics are highly dependent on the parameters which characterize agents' behavior (in particular the risk aversion coefficient and the chartist extrapolation parameter) as well as on the initial condition (in particular the initial wealth shares of fundamentalists and chartists). It is also shown that the for wide ranges of the parameters a (locally) stable fundamental steady state may coexist with a stable "nonfundamental" steady state, where price grows faster than the fundamental and only chartists survive in the long-run. In such cases, the role played by the initial condition is analysed by means of numerical investigations and graphical representation of the basins of attraction. Other dynamic scenarios include limit cycles, periodic orbits or more complex attractors, where in general both types of agents survive in the long run, with time varying wealth fractions.

A discrete time model of a financial market is proposed, where the time evolution of asset prices and wealth arises from the interaction of two groups of agents, fundamentalists and chartists. Each group allocates its wealth between a risky asset (stock) and an alternative asset (bond), and the two groups have heterogeneous expectations about returns. We assume that chartists compute expected returns by extrapolating past price changes, while fundamentalists form their expectations on the basis of their superior knowledge of fundamentals. Under the assumption that agents have CRRA utility, investors’ optimal demand for each asset depends on their wealth, and this results in growing price and wealth processes. The time evolution of the prices is modeled by assuming the existence of a market maker, who sets excess demand of each asset to zero at the end of each trading period by taking an off-setting long or short position. The market maker is assumed to adjust the price, in each period, partly on the basis of the excess demand and partly according to particular stabilizing policies. The model results in a high dimensional nonlinear discrete-time dynamical system with growing prices and wealth. Although the model is nonstationary, suitable changes of variables lead to a stationary model where the dynamic variables are actual and expected returns, fundamental/price ratios, and wealth proportions of chartists and fundamentalists. The steady states and other invariant sets of the model are determined, and important global dynamic phenomena are studied through numerical investigations. Stochastic simulations are also performed, that show the ability of the model to generate some of the characteristic features of financial time series.